Bedard-Hearn Michael J, Larsen Ross E, Schwartz Benjamin J
Department of Chemistry and Biochemistry, University of California, 607 Charles E. Young Drive East, Los Angeles, California 90095-1569, USA.
J Chem Phys. 2005 Dec 15;123(23):234106. doi: 10.1063/1.2131056.
The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence-the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state-and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrodinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.
区分非绝热混合量子/经典（MQC）模拟算法的关键因素在于它们如何纳入量子退相干——即经典原子核最终必定会使量子叠加态坍缩为纯态这一事实——以及它们如何对退相干对量子子系统和经典子系统的影响进行建模。大多数算法使用不同的机制来对纯量子基态之间的非绝热跃迁（“表面跳跃”）进行建模，并计算量子力学相位信息的损失（例如，密度矩阵非对角元素的衰减）。然而，在我们看来，这两个过程应该在对退相干的单一描述中统一起来。在本文中，我们从整个系统的密度矩阵出发，并对核波函数使用冻结高斯近似，以推导电子自由度的核诱导退相干速率。然后，我们将此退相干速率用作一种新的非绝热MQC分子动力学（MD）算法的基础，我们将其称为具有随机退相干的平均场动力学（MF-SD）。MF-SD首先根据含时薛定谔方程演化量子子系统，从而产生平均场动力学。MF-SD然后使用核诱导退相干速率在每个时间步随机确定系统是保持在相干混合态还是发生退相干。一旦确定系统应该退相干，量子子系统就会瞬间发生全波函数坍缩到其中一个绝热基态上，并且经典速度会被调整以守恒能量。因此，MF-SD将表面跳跃和退相干结合为一个单一的概念：MF-SD中的退相干不需要人工引入参考态、辅助轨迹或轨迹群，这也使得MF-SD在计算上比其他非绝热MQC MD算法高效得多。MF-SD中退相干的统一定义仅需要一个特设参数，该参数不可调整，而是由非绝热耦合的空间范围决定。我们使用MF-SD来解决一系列一维散射问题，发现MF-SD在定量上与几种现有的非绝热MQC MD算法一样准确，并且在某些问题上明显更准确。
